Reconstruction of mimetic gravity in a non-singular bouncing universe from quantum gravity

We illustrate a general reconstruction procedure for mimetic gravity. Focusing on a bouncing cosmological background, we derive general properties that must be satisfied by the function $f(\Box\phi)$ implementing the limiting curvature hypothesis. We show how relevant physical information can be extracted from power law expansions of $f$ in different regimes, corresponding e.g. to the very early universe or to late times. Our results are then applied to two specific models reproducing the cosmological background dynamics obtained in group field theory and in loop quantum cosmology, and we discuss the possibility of using this framework as providing an effective field theory description of quantum gravity. We study the evolution of anisotropies near the bounce, and discuss instabilities of scalar perturbations. Furthermore, we discuss two equivalent formulations of mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring two distinct time-varying gravitational "constants" in the cosmological equations.Comment: Invited article for the special issue "Progress in Group Field Theory and Related Quantum Gravity Formalisms" of the journal "Universe"; 21 pages, 2 figures; v2: matches published versio

Accelerated expansion of the Universe without an inflaton and resolution of the initial singularity from Group Field Theory condensates

We study the expansion of the Universe using an effective Friedmann equation obtained from the dynamics of GFT (Group Field Theory) isotropic condensates. The evolution equations are classical, with quantum correction terms to the Friedmann equation given in the form of effective fluids coupled to the emergent classical background. The occurrence of a bounce, which resolves the initial spacetime singularity, is shown to be a general property of the model. A promising feature of this model is the occurrence of an era of accelerated expansion, without the need to introduce an inflaton field with an appropriately chosen potential. We discuss possible viability issues of this scenario as an alternative to inflation.Comment: 14 pages, 4 figures, v2 revised to match published versio

Effective cosmological constant induced by stochastic fluctuations of Newton's constant

We consider implications of the microscopic dynamics of spacetime for the evolution of cosmological models. We argue that quantum geometry effects may lead to stochastic fluctuations of the gravitational constant, which is thus considered as a macroscopic effective dynamical quantity. Consistency with Riemannian geometry entails the presence of a time-dependent dark energy term in the modified field equations, which can be expressed in terms of the dynamical gravitational constant. We suggest that the late-time accelerated expansion of the Universe may be ascribed to quantum fluctuations in the geometry of spacetime rather than the vacuum energy from the matter sector.Comment: 10 pages, 1 figure, v2: added legend in Fig.1 and a referenc

Cosmological consequences of Quantum Gravity proposals

In this thesis, we study the implications of Quantum Gravity models for the dynamics of spacetime and the ensuing departures from classical General Relativity. The main focus is on cosmological applications, particularly the impact of quantum gravitational effects on the dynamics of a homogenous and isotropic cosmological background. Our interest lies in the consequences for the evolution of the early universe and singularity resolution, as well as in the possibility of providing an alternative explanation for dark matter and dark energy in the late universe. The thesis is divided into two main parts, dedicated to alternative (and complementary) ways of tackling the problem of Quantum Gravity. The first part is concerned with cosmological applications of background independent approaches to Quantum Gravity, both in the context of loop quantisation and in quantum geometrodynamics. Particularly relevant in this work is the Group Field Theory approach, which we use to study the effective dynamics of the emergent universe from a full theory of Quantum Gravity (i.e. without symmetry reduction). In the second part, modified gravity theories are introduced as tools to provide an effective description of quantum gravitational effects, e.g. by introducing new degrees of freedom and symmetries. Particularly relevant in this respect is local conformal invariance, which finds a natural realisation in the framework of Weyl geometry. We build a modified theory of gravity based on such symmetry principle, and argue that new fields in the extended gravitational sector may play the role of dark matter. New degrees of freedom are also natural in models with varying fundamental `constants', which we examine critically. Finally, we discuss prospects for future work and point at directions for the derivation of realistic cosmological models from Quantum Gravity candidates.Comment: PhD thesis, King's College London (supervisor: Mairi Sakellariadou), 282 pages, 20 figures; submitted in September 201

Local conformal symmetry in non-Riemannian geometry and the origin of physical scales

We introduce an extension of the Standard Model and General Relativity built upon the principle of local conformal invariance, which represents a generalization of a previous work by Bars, Steinhardt and Turok. This is naturally realized by adopting as a geometric framework a particular class of non-Riemannian geometries, first studied by Weyl. The gravitational sector is enriched by a scalar and a vector field. The latter has a geometric origin and represents the novel feature of our approach. We argue that physical scales could emerge from a theory with no dimensionful parameters, as a result of the spontaneous breakdown of conformal and electroweak symmetries. We study the dynamics of matter fields in this modified gravity theory and show that test particles follow geodesics of the Levi-Civita connection, thus resolving an old criticism raised by Einstein against Weyl's original proposal.Comment: 11 pages; v2: matches published version in EPJC; new title, includes new sections on the coupling of matter fields to the extended gravitational secto

Semiclassical solutions of generalized Wheeler-DeWitt cosmology

We consider an extension of WDW minisuperpace cosmology with additional interaction terms that preserve the linear structure of the theory. General perturbative methods are developed and applied to known semiclassical solutions for a closed Universe filled with a massless scalar. The exact Feynman propagator of the free theory is derived by means of a conformal transformation in minisuperspace. As an example, a stochastic interaction term is considered and first order perturbative corrections are computed. It is argued that such an interaction can be used to describe the interaction of the cosmological background with the microscopic d.o.f. of the gravitational field. A Helmoltz-like equation is considered for the case of interactions that do not depend on the internal time and the corresponding Green's kernel is obtained exactly.The possibility of linking this approach to fundamental theories of Quantum Gravity is investigated.Comment: 18 pages, 5 figure

Cosmological implications of interacting Group Field Theory models: cyclic Universe and accelerated expansion

We study the cosmological implications of interactions between spacetime quanta in the Group Field Theory (GFT) approach to Quantum Gravity from a phenomenological perspective. Our work represents a first step towards understanding Early Universe Cosmology by studying the dynamics of the emergent continuum spacetime, as obtained from a fundamentally discrete microscopic theory. In particular, we show how GFT interactions lead to a recollapse of the Universe while preserving the bounce replacing the initial singularity, which has already been shown to occur in the free case. It is remarkable that cyclic cosmologies are thus obtained in this framework without any a priori assumption on the geometry of spatial sections of the emergent spacetime. Furthermore, we show how interactions make it possible to have an early epoch of accelerated expansion, which can be made to last for an arbitrarily large number of e-folds, without the need to introduce an ad hoc potential for the scalar field.Comment: 11 pages, 6 figure